Abstract

Topological insulators constitute a new quantum phase of matter that is characterized by a band gap in the bulk, just like an ordinary insulator, but hosts gapless states on its surface. Illuminating a topological insulator by light is expected to lead to a unique current response due to the helical nature of the surface states. Such photocurrents flowing on the surface of a topological insulator will be spin-polarized and the ability to induce and control spin-polarized currents might make topological insulators valuable materials for spintronic devices. The surface photocurrent response would also be a tool for studying the dynamical properties of the topological surface states. In this thesis, we investigate the theory of photocurrent generation and relaxation in topological insulators. We first study photocurrent generation within a pure surface state model and find that minimal coupling between light and electrons leads to a vanishing photocurrent. For a finite photocurrent one has to consider the small Zeeman coupling between the light and the electron spin. Photocurrents on the surface of 3D topological insulators have been experimentally observed using laser energies larger than the bulk band gap. We thus extend our pure surface model and include the low-energy bulk states to account for excitations involving the surface Dirac cone and the bulk. We indeed find that photoinduced transitions between surface and bulk states can lead to a photocurrent which is several orders of magnitude larger than the effect in the pure surface model. We also investigate photocurrent relaxation by carrier-carrier scattering. While such scattering processes cannot relax current in quadratically dispersing systems, they do affect the current in the linearly dispersing surface states. We study the limit of a single particle-hole pair and analyze how scattering affects the individual electron and hole contributions to the current. We find that the effect of carrier-carrier scattering on the individual electron and hole currents strongly depends on the position of the Fermi level, even leading to an amplification of the electron current for positive Fermi energy. This results in a suppression of the relaxation of photocurrents carried by electron-hole pairs. Topologische Isolatoren beschreiben eine neue Phase der Materie, welche eine Bandlücke im Volumen, an der Oberfläche jedoch metallische Zustände aufweist. Bestrahlt man einen topologischen Isolator mit Licht, erwartet man, dass die helikalen Oberflächenzustände zu einzigartigen Photoströmen führen. Photoströme auf der Oberfläche sind spinpolarisiert. Die Möglichkeit spinpolarisierte Ströme zu kontrollieren könnte topologische Isolatoren zu wertvollen Materialien für Spintronikanwendungen machen. Außerdem ließe sich mit Photoströmen die dynamischen Eigenschaften von topologischen Isolatoren untersuchen. In der vorliegenden Arbeit untersuchen wir die Theorie der Anregung und Relaxation von Photoströmen in topologischen Isolatoren. Zuerst untersuchen wir die…